New Insight into H2S Sensing Mechanism of Continuous SnO2–CuO

Article pubs.acs.org/JPCC

New Insight into H2S Sensing Mechanism of Continuous SnO2−CuO Bilayer Thin Film: A Theoretical Macroscopic Approach Zhoubin Boroun,† Mohammad Ghorbani,*,†,‡ Ali Moosavi,§ and Raheleh Mohammadpour† †

Institute for Nanoscience and Nanotechnology, ‡Department of Materials Science and Engineering, and §Department of Mechanical Engineering, Sharif University of Technology, Tehran 11155-9466, Iran S Supporting Information *

ABSTRACT: SnO2−CuO is one the most promising systems for detection of detrimental H2S gas. Although previous experimental research has suggested a sulfidation reaction to explain selectivity toward H2S, little is known about the origin of change of electrical response of this system by changing the H2S gas concentration. In this study the relation between sensing response of continuous SnO2−CuO bilayer thin film and H2S gas concentration is computed based on changeability of chemical composition of covellite CuxS. For this purpose, chemical activity of sulfur as a function of atomic fraction in covellite copper sulfide is estimated using Gibbs energies of formation and chemical thermodynamics. By considering equilibrium between covellite and H2S, a relationship between chemical composition of the copper sulfide and concentration of the gas at 150 °C is obtained. Utilizing electronic physics and finite difference method, electrical response of the sensor as a function of H2S concentration is computed. Results show that increasing H2S concentration from 0.053 ppm to saturation value of 455 ppm changes chemical composition of the upper conductive covellite layer from Cu1.5S to CuS, which increases the response of the system. The model explains why SnO2−CuO systems can detect H2S gas from sub-ppm levels to hundreds of ppm without involving oxygen adsorption/ desorption phenomena. Finally, the theoretical response−concentration curve is compared with the previous experimental curve. Despite a few differences, the theoretical curve matches relatively well with the experimental one.

1. INTRODUCTION H2S is a toxic gas detrimental to human health as well as some of important industries, particularly oil and gas.1 Metal oxide semiconductors such as SnO2,2 ZnO,3 and CuO4 have been investigated for the detection of H2S. One of the most popular systems for sensing of this gas is SnO2−CuO, which (as far as we know) has been paid attention since 1992.5−9 High sensitivity at low concentrations (below 1 ppm),10 good selectivity,11 and fast speed12 (response time + recovery time) in sensing process of H2S gas are advantages of this system. Mechanisms of H2S sensing of the mentioned oxide system have been qualitatively investigated.5,6,13,14 SnO2 is an n-type semiconductor and CuO is a p-type one. Adding CuO to SnO2 causes the formation of a p−n junction that will lead to relatively high electrical resistance in the air. Upon exposure to H2S, CuO is transformed to metallic CuS in the covellite phase (Figure 1), which has a relatively good conductivity, by the following reaction CuO + H 2S → CuS + H 2O

Figure 1. Sulfidation of copper oxide in continuous SnO2−CuO bilayer (left) and chemical equilibrium between covellite copper sulfide and H2S gas (right).

to solo SnO2 layer, which is dependent on the gas concentration.13 XRD results of Manorama et al.6 indicated that CuO completely transforms to covellite copper sulfide upon exposure to H2S gas, which is consistent with the fact that increasing thickness or mass of CuO layer increases response time of the sensor10,15 (due to more reaction time). The main question here is what chemical composition the system might have at different H2S concentrations. Electrical resistance of

(1)

Reaction 1 causes a drastic decrease in electrical resistance of the system.5,6,13,14 Electrical resistance of the SnO2−CuO bilayer has been reported to reach stable values in the presence of H2S similarly © XXXX American Chemical Society

Received: February 12, 2016 Revised: March 31, 2016

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Figure 2. Molar Gibbs energies of copper sulfides (latest update for each) with three different chemical formulas, CuS, Cu1.1S, and Cu1.4S at 150 °C with respect to sulfur atomic fraction calculated from databases (a) formation and (b) mixing.

SnO2−CuO continuous bilayer has been reported to be almost insensitive to oxygen partial pressure.13 The existence of stable resistance, its dependency on H2S concentration, full sulfidation of CuO, and insensitivity of SnO2−CuO continuous bilayer toward oxygen partial pressure imply that instead of conventional equilibrium between oxygen adsorption and desorption surface reactions (which are responsible for sensitivity of solo SnO2 thin film)16 another mechanism must be responsible for changes of response toward H2S concentration. There exists abundant experimental research about the application of SnO2−CuO for H2S sensing in literature;5−14 however, for further progress about the performance of this promising system, some important questions must be answered. One of these questions is what kind of chemistry is responsible for δS/ δXH2S (S is response and XH2S is concentration of H2S) in SnO2−CuO continuous bilayer and in general why SnO2−CuO systems can detect H2S from sub-ppm levels7,10,17,18 to hundreds of ppm.6,12,13 There are two ways to answer such questions, in situ chemical analysis and theoretical modeling; however, it is difficult to perform accurate spectroscopic chemical analysis under practical conditions in which atmospheric pressure and corrosive H2S gas exist. Although H2S sensing properties of Cu−SnO2 (Cu solved in SnO2 instead of forming oxide heterojunction)19 and ZnO20 have been theoretically investigated, we were not able to find any report about theoretical modeling for SnO2−CuO system. Therefore, to give experimental researchers better insight, the main objective of this paper is to numerically compute the response of the continuous layer of CuO on the SnO2 layer as a function of H2S concentration based on the sulfidation mechanism demonstrated in Figure 1.

Apparently a nearly linear relation between ΔGf and sulfur atomic fraction (Xs) may exist ΔGf ≈ aXs + b

For CuxS, Xs = ΔGm =

1 , 1+x

(2)

and thus

ΔGf = XsΔGf 1+x

(3)

Therefore, an approximately parabolic relation between molar Gibbs energy of mixing and sulfur atomic fraction in covellite may exist. This indicates that the two elements (Cu and S) may have the ability to form solid solution in covellite according to solutions thermodynamics,23 which would result in tunability of chemical composition in this phase. Interestingly, Putnis et al.24 concluded that more covellite-based copper sulfide may exist and the possibility of forming the solid solution was suggested. Xie et al.25 proved that covellite copper sulfide nanocrystals have tunable composition (a prominent property of any solid solution). They also found that increasing the Cu content of CuxS makes it less metallic (optically),25 which is somewhat consistent with the fact that electrical resistivity of copper sulfide depends on its chemical composition and as a rule it increases as the Cu content increases.26−28 Hence, the framework of this numerical model is based on the following assumptions and considerations (1) CuO transforms covellite copper sulfide (Figure 1).6 (2) The covellite copper sulfide with chemical formula of CuxS is thermodynamically in chemical equilibrium with H2S gas (Figure 1). This would explain the existence of stable resistance in the presence of the gas, which has been experimentally observed.11,13 (3) As H2S concentration increases, sulfur atomic fraction in copper sulfide increases, and thus that of Cu decreases, which makes the sensor electrically more conductive and therefore sensitivity increases. It should be noted that the number of Cu atoms is constant in this process, and hence x in CuxS is merely the Cu/S atomic ratio and the number of sulfur atoms is changeable. (4) There is a critical H2S concentration in which sulfur atomic fraction in copper sulfide reaches its maximum value, and under atmospheric pressure this value is 0.5.21 Thus, at H2S concentrations equal to or above this critical value the sulfur content of copper sulfide (CuS) cannot be further increased. (5) It is known that oxygen plays an essential role during the recovery process;5 however, because a sulfidation reaction occurs, we were not able to assess what role oxygen plays

2. MODEL AND COMPUTATIONAL DETAILS 2.1. Theoretical Background. According to the Cu−S phase diagram,21 copper and sulfur can form solid solutions in forms of dignetite, djurlite, α-chalcocite, and β-chalcocite crystal structures but apparently not in covellite; however, it had been reported that beside CuS, two other copper sulfides with crystal structure resemble covellite, but different chemical formulas of Cu1.1S (Cu9S8, Blaubleibender covellite I) and Cu1.4S (Cu39S28, Blaubleibender covellite II) also exist.21 Figure 2a,b shows molar Gibbs energy of formation (ΔGf) and molar Gibbs energy of mixing (ΔGm) at 150 °C with respect to sulfur atomic fraction for covellite with three different chemical formulas, CuS,22 Cu1.1S, and Cu1.4S.21 B

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this paper. Hence Taylor expansions (also suggested by Margules)23 are applied to estimate relation between activity coefficient and atomic fraction of sulfur in covellite. Utilizing the Gibbs−Duhem equation,23 Taylor expansions, and the Gibbs energies of mixing in Figure 2b, the activity coefficient of sulfur is calculated as follows

during the response process. Therefore, while it is possible that electrical resistance of the bilayer in gas depends on both H2S and O2 concentrations, the reactivity of oxygen is not considered in this model. In addition, for bilayers response speed is reported to be considerably greater than recovery speed.13,17 Thus, it is reasonable to hypothesize that sulfidation speed is much greater than oxidation speed in the case of bilayers. Hence in this study we assume that O2 cannot kinetically compete with H2S. Therefore, the model consists of these steps: (1) Estimating a relation between chemical composition (atomic fraction of sulfur) of covellite CuxS and H2S gas concentration. (2) Estimating a relation between electrical conductivity of covellite CuxS and atomic fraction of sulfur. (3) Calculating the ratio of electrical resistance of sensor in air to that in gas (response or sensitivity). 2.2. Chemical Thermodynamics. Most of the calculations were performed at 423.15 K (150 °C) because this was the working temperature reported by Chowdhuri et al.13 for both continuous bilayer and dotted systems, and also Liu et al.14 reported that this working temperature was independent of H2S concentration. Under equilibrium conditions the following reaction between H2S and H2 gases and sulfur atoms in covellite copper sulfide is considered [S]in CuxS + H2(gas) ↔ H 2S(gas)

⎛ ⎛ 3 ⎞⎛ 1⎞ 1 ⎞2 ln(γS) = α0 + ⎜ −α2 − α3⎟⎜XS − ⎟ + α2⎜XS − ⎟ ⎝ ⎝ 4 ⎠⎝ 2⎠ 2⎠ ⎛ 1 ⎞3 + α3⎜XS − ⎟ ⎝ 2⎠

with α0 = −3.49399, α2 = −7.37439, and α3 = −108.51. More details have been provided in the Supporting Information. Thus, chemical activity of sulfur in covellite copper sulfide was estimated, and by inputting eq 9 in eq 8 and eq 8 in eq 7, a relation between atomic fraction of sulfur in covellite copper sulfide and H2S gas concentration at 150 °C was obtained. 2.3. Conductivity of Covellite Copper Sulfide. As mentioned in the Theoretical Background section, increasing x in CuxS decreases its electrical resistivity; however, to calculate the response of the sensor as a function of H2S gas concentration, a quantitative relation between chemical composition and electrical conductivity of copper sulfide in the covellite phase (σCuxS) must be estimated. For this purpose, both decrease in number (Nf(x)) and mobility (μf(x)) of free charge carriers in covellite by increasing copper content were taken into account

(4)

By referring to equilibrium thermodynamic rules this relation exists between species23 ⎛ aH S ⎞ Δr G (T ) = − RT ln⎜⎜ 2 ⎟⎟ ⎝ a H2as ⎠

σCuxS = Nf (x)μf (x)

°

(6)

XH2S and XH2 are atomic fractions of H2S and H2 in the gas phase, respectively. At T = 423.15 K, ΔrG0(423.15) = −38 368(J/mol),22 and by considering atmospheric air composition, XH2 = 0.55 ppm,29 eq 6 becomes X H2S(ppm) = 29975as

S=

R air R gas

(11)

Rair and Rgas are stable electrical resistances of the sensor in air and gas, respectively. According to the model, Rair is electrical resistance of SnO2−CuO bilayer and Rgas is that of SnO2−CuxS. Because R = V/I, the response can be redefined as

(7)

Chemical activity of sulfur can be written as a function of its atomic fraction23 as = γsXs

(10)

Utilizing changes in intensities of localized surface plasmon resonance peaks,25 an empirical relation between number of free charge carriers and chemical composition of covellite was obtained. Then, a simple host−impurity solid solution model31 was applied to approximate the relation between reduction of free charge carrier mobility and excess copper content in covellite. Finally, resistivity and conductivity of covellite CuxS as a function of chemical composition were estimated. Full details have been provided in the Supporting Information. By using the result of chemical thermodynamics, a numerical relation between conductivity of covellite CuxS and H2S gas concentration was estimated. 2.4. Response of the Sensor. Response of an electrical DC gas sensor (S) is usually defined as

(5)

ΔrG0(T) is standard Gibbs energy (J/mol) of reaction 4, R is the universal gas constant (8.314 (J/(mol·k)), T is temperature (K), aH2S and aH2 are chemical activities of H2S and H2 in gas phase, respectively, and as is chemical activity of sulfur in covellite copper sulfide. In eq 5, by assuming the ideal gas behavior (agas = XgasP) and atmospheric condition (P = 1 atm), a linear relation between chemical activity of sulfur and atomic fraction of H2S is obtained ⎛ Δ G 0 (T ) ⎞ ⎟X H as X H2S = exp⎜ − r ⎝ 8.314T ⎠ 2

(9)

S=

(8)

γs is the chemical activity coefficient of sulfur in covellite copper sulfide. The activity coefficient itself is a function of atomic fraction.23 Because the main objective of this model is to provide new macroscopic insight into the H2S sensing process of the SnO2−CuO system and also there is still a considerable confusion about electronic structure of covellite,30 calculation of theoretical Gibbs energy of mixing is beyond the scope of

ISnO2 − CuxS ISnO2 − CuO

(12)

ISnO2−CuO and ISnO2−CuxS are steady-state electrical currents of the sensor in air and gas, respectively. Electrical current (I) is integration of current density (Jx) across direction y

I= C

∫ Jx ·dy

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Because under atmospheric pressure the minimum value of x in copper sulfide is 1,21,26 there exists a saturation H 2S concentration at 455 ppm at which x is equal to 1 and sulfur content of CuS cannot be increased further by increasing H2S concentration. Figure 5 depicts eq 10 and indicates that σCuxS

To calculate current density, we must know spatial distributions of electrical potential (V), electron density (n), and hole density (p). Figure 3 depicts the geometry of the bilayer thin film system used in this model.

Figure 3. Geometry of bilayer thin film system used in the model (Lx = 300 μm, Ly = 100 nm, Ly1 = 10 nm, Lx1 = 1/3Lx, Lx2 = 2/3Lx, Ly2 = Ly + Ly1). Figure 5. Estimated relation between electrical conductivity of covellite copper sulfide and sulfur atomic fraction.

Poisson, continuity, and Laplace equations were solved utilizing finite difference method to obtain steady-state electrical currents in air and gas. It should be mentioned that sensor configuration in Figure 3 is a very simplified case and in reality the interface between two oxides is not flat and also part of CuO may penetrate between SnO2 grains; however, because it is highly difficult to solve electrical equations for a real bilayer geometry (due to mathematically complex boundary conditions) and also main purpose of this model is to provide new macroscopic insight into the dependency of the response of the SnO2−CuO bilayer toward H2S gas concentration and not toward other variables (such as SnO2 grain size), some geometrical simplifications were inevitable. Details of electrical calculations with corresponding boundary conditions and materials electronic constants have been presented in the Supporting Information. By inputting results of pervious sections into electrical calculations, the response of the sensor as a function of H2S gas concentration, S(XH2S), at 150 °C was calculated.

increases by increasing sulfur atomic fraction and vice versa. Figure 6 is a combination of results of Figures 4 and 5, which demonstrate the dependency of conductivity of covellite copper sulfide toward H2S gas concentration.

Figure 6. Relation between electrical conductivity of covellite copper sulfide and H2S gas concentration.

3. RESULTS AND DISCUSSION 3.1. Results of Computation and Interpretation. Figure 4 shows the atomic fraction of sulfur in covellite copper sulfide as a function of H2S gas concentration at 150 °C according to eq 7. Referring to reaction 4, increasing H2S gas concentration from 0.053 to 455 ppm increases the sulfur atomic fraction in covellite CuxS from 0.4 to 0.5 which decreases x from 1.5 to 1.

Figure 7 shows the computed response (sensitivity) of the SnO2−CuO thin-film bilayer system as a function of H2S concentration at 150 °C. Although CuxS film is not in direct contact with electrodes, clearly electrical conduction through this layer dominates the conduction of the whole system so that

Figure 4. Estimated relation between sulfur atomic fraction in covellite copper sulfide and H2S gas concentration 150 °C.

Figure 7. Computed response (sensitivity) of SnO2−CuO bilayer thin film as a function of H2S concentration at 150 °C. D

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Figure 10. Comparison between theoretical and experimental response−concentration curves.

CuxS is equal to 1.5 at 30, 100, 150, 200, and 300 °C, respectively. Localized surface plasmon resonance analysis performed by Xie et al.25 proved that even covellite Cu1.5S possesses metallic property (although weaker than Cu1.1S and Cu1.3S but considerably stronger than semiconducting Cu2S). Therefore, calculations predict the existence of a metallic phase (and consequently relatively good conductivity with respect to semiconducting CuO) at sub-ppm level of H2S gas. Hence our model can explain sub-ppm (or even tens of ppb) level detection of H2S gas, which has been experimentally reported for bilayer at 200 °C17 and also other systems of SnO2−CuO at 100,10 35,18 and 300 °C.7 3.2.3. Response−Concentration Curve. Referring to Figure 7, the response of the system at 455 ppm reaches its maximum value. Let’s call this quantity “Smax”. Figure 10 shows comparison between the theoretical response−concentration curve with the experimental one reported by Chowdhuri et al.13 for continuous layer of CuO on SnO2 (not dotted CuO nor solo SnO2). For a better comparison, normalized curves (S/ Smax) are demonstrated in Figure 11. Although there are few differences, the theoretical curve matches the experimental curve relatively well.

Figure 8. Color contours of spatial distribution of electrical potential in the sensor (a) in air and (b) in H2S.

It means that there is relatively high electrical flow along the metallic layer. For better understanding, a brief qualitative illustration of the whole computational results with equivalent electrical circuits has been demonstrated in Figure 9. As H2S

Figure 9. Schematic illustration of sensing process mechanism at different H2S concentrations with equivalent electrical circuit.

concentration increases, the sulfur atomic fraction in copper sulfide increases, and thus that of Cu decreases, which makes the top covellite CuxS layer electrically more conductive and therefore resistance of the whole sensor in the presence of H2S (Rgas) decreases, which according to eq 11, increases the response of the sensor. 3.2. Comparison with Previous Experimental Results. 3.2.1. Detection up to Hundreds of ppm. At 150 °C, saturation concentration of 455 ppm of H2S gas was estimated, which is comparable to saturation concentration around 500 ppm as experimentally reported by Chowdhuri et al.13 for continuous layer of CuO on SnO2 (not dotted CuO nor solo SnO2) at this temperature (Figure 10). In addition, detection of H2S up to hundreds of ppm level via SnO2−CuO system has also been reported by Wang et al.12 and Manorama et al.6 3.2.2. Sub-ppm Detection. According to our calculations, at 0.003, 0.02, 0.053, 0.1, and 0.3 ppm of H2S gas, x in covellite

Figure 11. Comparison between theoretical and experimental normalized response−concentration curves. E

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(7) Choi, K. I.; Kim, H. J.; Kang, Y. C.; Lee, J. H. Ultraselective and Ultrasensitive Detection of H2S in Highly Humid Atmosphere Using CuO-Loaded SnO2 Hollow Spheres for Real-Time Diagnosis of Halitosis. Sens. Actuators, B 2014, 194, 371−376. (8) Zhang, S.; Zhang, P.; Wang, Y.; Ma, Y.; Zhong, J.; Sun, X. Facile Fabrication of a Well-Ordered Porous Cu-Doped SnO2 Thin Film for H2S Sensing. ACS Appl. Mater. Interfaces 2014, 6, 14975−14980. (9) Van Toan, N.; Chien, N. V.; Van Duy, N.; Vuong, D. D.; Lam, N. H.; Hoa, N. D.; Van Hieu, N.; Chien, N. D. Scalable Fabrication of SnO2 Thin Films Sensitized with CuO Islands for Enhanced H2S Gas Sensing Performance. Appl. Surf. Sci. 2015, 324, 280−285. (10) Zhao, Y.; Li, J.; Gao, X.; Jia, J. Enhanced H2S Sensing Properties of Porous SnO2 Nanofibers Modified with CuO. Proc. Int. Meet. Chem. Sens., 12th 2012, 8, 718−721. (11) Verma, M. K.; Gupta, V. A Highly Sensitive SnO2−CuO Multilayered Sensor Structure for Detection of H2S Gas. Sens. Actuators, B 2012, 166, 378−385. (12) Wang, S.; Xiao, Y.; Shi, D.; Liu, H. K.; Dou, S. X. Fast Response Detection of H2S by CuO-doped SnO2 Films Prepared by Electrodeposition and Oxidization at Low Temperature. Mater. Chem. Phys. 2011, 130, 1325−1328. (13) Chowdhuri, A.; Sharma, P.; Gupta, V.; Sreenivas, K.; Rao, K. V. H2S Gas Sensing Mechanism of SnO2 Films with Ultrathin CuO Dotted Islands. J. Appl. Phys. 2002, 92, 2172−2180. (14) Liu, J.; Huang, X.; Ye, G.; Liu, W.; Jiao, Z.; Chao, W.; Zhou, Z.; Yu, Z. H2S Detection Sensing Characteristic of CuO/SnO2 Sensor. Sensors 2003, 3, 110−118. (15) Gupta, V.; Mozumdar, S.; Chowdhuri, A.; Sreenivas, K. Influence of CuO Catalyst in the Nanoscale range on SnO2 Surface for H2S Gas Sensing Applications. Pramana 2005, 65, 647−652. (16) Yamazoe, N.; Shimanoe, K. Theory of power laws for semiconductor gas sensors. Sens. Actuators, B 2008, 128, 566−573. (17) Jianping, L.; Yue, W.; Xiaoguang, G.; Qing, M.; Li, W.; Jinghong, H. H2S sensing properties of the SnO2 -based thin films. Sens. Actuators, B 2000, 65, 111−113. (18) He, L.; Jia, Y.; Meng, F.; Li, M.; Liu, J. Development of sensors based on CuO-doped SnO2 hollow spheres for ppb level H2S gas sensing. J. Mater. Sci. 2009, 44, 4326−4333. (19) Wei, W.; Dai, Y.; Huang, B. Role of Cu Doping in SnO2 Sensing Properties Toward H2S. J. Phys. Chem. C 2011, 115, 18597−18602. (20) Iversen, K. J.; Spencer, M. J. S. Effect of ZnO Nanostructure Morphology on the Sensing of H2S Gas. J. Phys. Chem. C 2013, 117, 26106−26118. (21) Chakrabarti, D. J.; Laughlin, D. E. The Cu-S System. Bull. Alloy Phase Diagrams 1983, 4, 254−270. (22) Kubaschewski, O.; Aloock, C.; Spencer, P. J. Materials Thermochemistry, 6th ed; Pergamon Press: Oxford, U.K., 1993. (23) Gaskell, D. R. Introduction to Thermodynamics of Materials, 3rd ed; Taylor & Francis: Washington, DC, 1995. (24) Putnis, A.; Grace, J.; Cameron, W. E. Blaubleibender Covellite and Its Relationship to Normal Covellite. Contrib. Mineral. Petrol. 1977, 60, 209−217. (25) Xie, Y.; Riedinger, A.; Prato, M.; Casu, A.; Genovese, A.; Guardia, P.; Sottini, S.; Sangregorio, C.; Miszta, K.; Ghosh, S.; et al. Copper Sulfide Nanocrystals with Tunable Composition by Reduction of Covellite Nanocrystals with Cu+ Ions. J. Am. Chem. Soc. 2013, 135, 17630−17637. (26) Ancutiene, I.; Janickis, V.; Ivanauskas, R. Formation and characterization of conductive thin layers of copper sulfide (CuxS) on the surface of polyethylene and polyamide by the use of higher polythionic acids. Appl. Surf. Sci. 2006, 252, 4218−4225. (27) Rodríguez-Lazcano, Y. R.; Martínez, H.; Calixto-Rodríguez, M.; Núñez Rodríguez, A. N. Properties of CuS Thin Films Treated in Air Plasma. Thin Solid Films 2009, 517, 5951−5955. (28) Johansson, J.; Kostamo, J.; Karppinen, M.; Niinisto, L. Growth of Conductive Copper Sulfide Thin Films by Atomic Layer Deposition. J. Mater. Chem. 2002, 12, 1022−1026. (29) http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html (accessed 7/21/2015).

4. CONCLUSIONS In summary we presented an interdisciplinary macroscopic model to explain origin of increase in sensing response of SnO2−CuO continuous bilayer thin film by increasing H2S gas concentration without involving oxygen adsorption/desorption phenomena. At 150 °C, by increasing the concentration of the gas from 0.053 ppm to saturation value of 455 ppm, Cu/S atomic ratio in covellite phase changes from 1.5 to 1, which will increase the conductivity of the top layer and the response of the system. Therefore, the model explains why SnO2−CuO systems can detect H2S gas from sub-ppm levels to hundreds of ppm, which is due to thermodynamical equilibrium between covellite copper sulfide with tunable composition and H2S gas. Although the computational response−concentration curve did not exactly match with the experimental one, as the first theoretical curve, it described the H2S sensing behavior of the continuous layer of CuO on SnO2 relatively well. We hope this information assists experimental researchers for better design of the SnO2−CuO H2S sensor.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b01504. Details of estimating relation between chemical activity coefficient of sulfur and its atomic fraction in covellite, details of estimating relation between electrical conductivity and chemical composition of covellite CuxS, and details of electrical calculations with corresponding boundary conditions, finite difference method, and materials electronic constants. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +98 21 6600 5717. Tel: +98 21 6616 5219. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful to all of Institute of Nanoscience and Nanotechnology’s personnel for their support. REFERENCES

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